# Population Simulation Using MatLab - PowerPoint PPT Presentation

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Population Simulation Using MatLab. Jie Ma EPS 109 Professor. Militzer. Fox vs. Rabbit. 1. Predator-prey Function: (Lab3) Predator : Fox Prey : Rabbit 2. Solve Differential Equation (Lab 13) Runge Kutta Method Stable when dx/ dt = 0; dr / dt = 0;. Population changes .

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Population Simulation Using MatLab

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## Population Simulation Using MatLab

Jie Ma

EPS 109

Professor. Militzer

### Fox vs. Rabbit

• 1. Predator-prey Function: (Lab3)

• Predator: Fox

• Prey: Rabbit

• 2. Solve Differential Equation (Lab 13)

• RungeKutta Method

• Stable when dx/dt = 0; dr/ dt = 0;

### Population changes

How to visualize?

Red: Fox

Blue: rabbit

Reference the Random walk Lab5:

Generate a white matrix

to represent the total population

Using Red grad to represent fox

population and blue grad to represent the rabbit population

Use random number to generate a random location of Fox or Rabbit.

• Red for Fox and Blue for rabbit

• When the rabbit population increase, the fox population increase, and rabbit population decrease.

for j = 1:numFox

%calculte the index of the location

while 1

randloc = round(rand()*maxPoP);

rand_row = round(mod(randloc,sn))+1;

rand_col = round(randloc/sn)+1;

%if the poistion has already be not been taken, reject to move

if(A(rand_row,rand_col,2) == 255)

A(rand_row,rand_col,1) = 255;

A(rand_row,rand_col,2) = 0;

A(rand_row,rand_col,3) = 0;

break

end

end

end

### Peppered Moth evolution

X for bird: dx/dt= (-d +e * y+ et *z) * x;

Y for White Moth: dy/dt= (kr*( m –y )- c * x) *y;

Z for Bluemoth: dz/dt= (kt*(mt- z)-ct* x )* z;

C > Ct

Background color : gray

Yellow: white peppered moth

Black: black peppered moth

• Their dark color blend them in the polluted trees and makes it

• difficult to find by their predators. As a result they are more likely to

• survive and reproduce. As a result, the black moth population increase.